An experiment measures quantities a, b, and c, and then X is calculated from X=(a1 / 2 b2/c3). If the percentage errors in a, b, and c are ± 1 %, ± 3 %, and ± 2 %, respectively, then the percentage error in X can be

Question

An experiment measures quantities a, b, and c, and then X is calculated from X=(a1 / 2 b2/c3). If the percentage errors in a, b, and c are ± 1 %, ± 3 %, and ± 2 %, respectively, then the percentage error in X can be (A) ± 12.5 % (B) ± 7 % (C) ± 1 % (D) ± 4 %

Tardigrade Admin · Accepted Answer

X=(a1 / 2 b2/c3) (Δ X/X) × 100 =(1/2) (Δ a/a) × 100+2 (Δ b/b) × 100+3 (Δ c/c) × 100 =(1/2) × 1+2 × 3+3 × 2=12.5 %

Q. An experiment measures quantities $a, b$ , and $c$ , and then $X$ is calculated from $X = \frac{a ^{1/2} b ^{2}}{c ^{3}}$ . If the percentage errors in $a, b$ , and $c$ are $\pm 1%, \pm 3%$ , and $\pm 2%$ , respectively, then the percentage error in $X$ can be

$\pm 12.5%$

$\pm 7%$

$\pm 1%$

$\pm 4%$

$X = \frac{a ^{1/2} b ^{2}}{c ^{3}}$
$\frac{Δ X}{X} \times 100 = \frac{1}{2} \frac{Δ a}{a} \times 100 + 2 \frac{Δ b}{b} \times 100 + 3 \frac{Δ c}{c} \times 100$
$= \frac{1}{2} \times 1 + 2 \times 3 + 3 \times 2 = 12.5%$

Q. An experiment measures quantities a,b, and c, and then X is calculated from X=c3a1/2b2​. If the percentage errors in a,b, and c are ±1%,±3%, and ±2%, respectively, then the percentage error in X can be

±12.5%

±7%

±1%

±4%